Graph, fully connected

In the above MILP-optimization problem, Euler s theorem for the generation of stable and feasible molecular structures (fully connected graphs) needs to be added as a condition in order to ensure the generation of chemically feasible molecules. This condition is mathematically formulated as,... 

The Bivariate Marginal Distribution Algorithm (BMDA) [14] is an example of a second order model. It does not build a fully connected model like the HEDA, but discovers a sparse set of second order dependencies between variable pairs. The sparse nature of the connections means that subsets of variables may be completely separate from the rest, meaning that a set of graphs (known as a forest) is produced. The more sparse the network, the lower its capacity for storing attractors. The connections in the BMDA are conditional probabilities, making the model more akin to a Bayesian network, whereas the HEDA structure is more like that of a Markov Random Field. 

A multilayer perceptron (MLP) is a feed-forward artificial neural network model that maps sets of input data onto a set of suitable outputs (Patterson 1998). A MLP consists of multiple layers of nodes in a directed graph, with each layer fully connected to the next one. Except for the input nodes, each node is a neuron (or processing element) with a nonlinear activation function. MLP employs a supervised learning techruque called backpropagation for training the network. MLP is a modification of the standard linear perceptron and can differentiate data that are not linearly separable. 

The graph of the bond network is simple and contains all the necessary chemistry. It is fully defined by the atomic valences and the connections between... 

In bond graphs of hybrid system models, some storage elements in integral causality may be connected to a detector only via a causal path through a switch model Sw m or even through several switch models. Clearly, the necessary reachability condition is only satisfied when the switch involved in the causal path is closed. That is, a model is not fully state-observable in those system modes in which a switch being part of the only causal path from a storage element to a detector is off, i.e. m = 0 for the switched MTF of that switch model. 

Since the boundaries of the sample are always parallel to the x-, y- and z-coordinales the strains e, and , are principal strains and in combination with the principal stresses the stress-strain-state is fully determined. The line connecting all strain states in an Cy, e -strain graph is called the strain path. Accordingly the line connecting all stress states in a stress graph is called stress path. Strain paths and stress paths are plotted in two dimensional diagramins for convenience and because no strain is applied in the z direction. Every strain path results in a specific stress path and is therefore called associated stress path. 

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